Question

The figure below represents a triangular flower garden ABC in which AB = 4m, BC = 5and ∠BCA =30 degrees . Point D lies on AC such that BD = 4 m and ∠BDC is obtuse.
Find, correct to 2 decimal places:
(a) the length of AD;
(b) the length of DC;

Answer 1

As I posted earlier,

calling the angle A,B,C as usual in a diagram, use the law of sines to find that
sin(∠BDC)/5 = sin(30)/4
so, sin ∠BDC = 5/8
But you want the obtuse angle.
Now you know that ∠BDA = 180 - ∠BDC
And, since triangle BDA is isosceles, ∠DAB = ∠BDA
Now you can find ∠B, and use the law of sines to find the other sides.
And recall that in any triangle ABC, the area = 1/2 ab sinC

So, where do you get stuck? Did you draw the triangle to get an idea what's going on?

Answer 2

Both. how to use law of sin
(a) The length of AD;
AD/4 =
(b) the length of DC